Inversion Theorem Based Kernel Density Estimation for the Ordinary Least Squares Estimator of a Regression Coefficient

Dongliang Wang and Alan D. Hutson

Communications in Statistics - Theory and Methods, 2015, vol. 44, issue 8, 1571-1579

Abstract: The traditional confidence interval associated with the ordinary least squares estimator of linear regression coefficient is sensitive to non-normality of the underlying distribution. In this article, we develop a novel kernel density estimator for the ordinary least squares estimator via utilizing well-defined inversion based kernel smoothing techniques in order to estimate the conditional probability density distribution of the dependent random variable. Simulation results show that given a small sample size, our method significantly increases the power as compared with Wald-type CIs. The proposed approach is illustrated via an application to a classic small data set originally from Graybill (1961).

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:taf:lstaxx:v:44:y:2015:i:8:p:1571-1579

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DOI: 10.1080/03610926.2013.781633

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